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326_midterm-10

# 326_midterm-10 - UBC ECONOMICS 326 003 2010 MIDTERM...

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UBC, ECONOMICS 326 - 003 2010 MIDTERM EXAMINATION There are 3 questions (100 points total). You have 80 minutes. Answer all questions. Question 1. Consider a simple linear regression model: Y i = β 0 + β 1 X i + U i , i = 1 , . . . , n ; β 0 6 = 0; E ( U i | X 1 , . . . , X n ) = 0 . Define ˆ β 1 = n i =1 ( X i - ¯ X ) Y i n i =1 ( X i - ¯ X ) 2 and ˆ β 0 = ¯ Y - ˆ β 1 ¯ X, ˜ β 1 = n i =1 X i Y i n i =1 X 2 i and ˜ β 0 = 0 , where ¯ X = n - 1 n i =1 X i . Define also ˆ U i = Y i - ˆ β 0 - ˆ β 1 X i , ˜ U i = Y i - ˜ β 1 X i . For each of the following statements, indicate true or false and explain your answers. (a) (6 points) n i =1 ˆ U i = 0. (b) (6 points) n i =1 ˜ U i = 0. (c) (6 points) n i =1 U i = 0. (d) (6 points) E ( U i X 4 i ) = 0. (e) (6 points) In this model, ˆ β 1 is the OLS estimator, and therefore the Gauss- Markov Theorem implies that V ar ˆ β 1 | X 1 , . . . , X n V ar ˜ β 1 | X 1 , . . . , X n . Assume that errors U i ’s are homoskedastic and there is no serial correlation. 1

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Question 2. (a) (40 points) Find A-D in the Stata output below. The number of ob- servations is 29. (b) (5 points) According to the results, does x affect y? Explain. ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | A .373891 B
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326_midterm-10 - UBC ECONOMICS 326 003 2010 MIDTERM...

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